A three domain covariance framework for EEG/MEG data

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.Comment: 25 pages, 8 figures, 1 tabl

A non-Markovian model for cell population growth: speed of convergence and central limit theorem

In De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data

Wild Bootstrap for Counting Process-Based Statistics

The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper consists of two parts: in Part~I, a general framework is developed in which the large sample properties are established in a unified way by using martingale structures. The framework includes most of the well-known non- and semiparametric statistical methods in time-to-event analysis and parametric approaches. In Part II, the Fine-Gray proportional sub-hazards model exemplifies the theory for inference on cumulative incidence functions given the covariates. The model falls within the framework if the data are censoring-complete. A simulation study demonstrates the reliability of the method and an application to a data set about hospital-acquired infections illustrates the statistical procedure.Comment: 2 parts, 115 pages, 2 figures, 13 table

Inference via Wild Bootstrap and Multiple Imputation under Fine-Gray Models with Incomplete Data

Fine-Gray models specify the subdistribution hazards for one out of multiple competing risks to be proportional. The estimators of parameters and cumulative incidence functions under Fine-Gray models have a simpler structure when data are censoring-complete than when they are more generally incomplete. This paper considers the case of incomplete data but it exploits the above-mentioned simpler estimator structure for which there exists a wild bootstrap approach for inferential purposes. The present idea is to link the methodology under censoring-completeness with the more general right-censoring regime with the help of multiple imputation. In a simulation study, this approach is compared to the estimation procedure proposed in the original paper by Fine and Gray when it is combined with a bootstrap approach. An application to a data set about hospital-acquired infections illustrates the method.Comment: 32 pages, 2 figures, 1 tabl

Novel Candidate Genes Associated with Hippocampal Oscillations

The hippocampus is critical for a wide range of emotional and cognitive behaviors. Here, we performed the first genome-wide search for genes influencing hippocampal oscillations. We measured local field potentials (LFPs) using 64-channel multi-electrode arrays in acute hippocampal slices of 29 BXD recombinant inbred mouse strains. Spontaneous activity and carbachol-induced fast network oscillations were analyzed with spectral and cross-correlation methods and the resulting traits were used for mapping quantitative trait loci (QTLs), i.e., regions on the genome that may influence hippocampal function. Using genome-wide hippocampal gene expression data, we narrowed the QTLs to eight candidate genes, including Plcb1, a phospholipase that is known to influence hippocampal oscillations. We also identified two genes coding for calcium channels, Cacna1b and Cacna1e, which mediate presynaptic transmitter release and have not been shown to regulate hippocampal network activity previously. Furthermore, we showed that the amplitude of the hippocampal oscillations is genetically correlated with hippocampal volume and several measures of novel environment exploration

LLM3D: a log-linear modeling-based method to predict functional gene regulatory interactions from genome-wide expression data

All cellular processes are regulated by condition-specific and time-dependent interactions between transcription factors and their target genes. While in simple organisms, e.g. bacteria and yeast, a large amount of experimental data is available to support functional transcription regulatory interactions, in mammalian systems reconstruction of gene regulatory networks still heavily depends on the accurate prediction of transcription factor binding sites. Here, we present a new method, log-linear modeling of 3D contingency tables (LLM3D), to predict functional transcription factor binding sites. LLM3D combines gene expression data, gene ontology annotation and computationally predicted transcription factor binding sites in a single statistical analysis, and offers a methodological improvement over existing enrichment-based methods. We show that LLM3D successfully identifies novel transcriptional regulators of the yeast metabolic cycle, and correctly predicts key regulators of mouse embryonic stem cell self-renewal more accurately than existing enrichment-based methods. Moreover, in a clinically relevant in vivo injury model of mammalian neurons, LLM3D identified peroxisome proliferator-activated receptor γ (PPARγ) as a neuron-intrinsic transcriptional regulator of regenerative axon growth. In conclusion, LLM3D provides a significant improvement over existing methods in predicting functional transcription regulatory interactions in the absence of experimental transcription factor binding data